One way you can develop empathy is to start with small sentient beings like ants and insects. Really attend to them and recognize that they too wish to find happiness, experience pleasure, and be free of pain. Start there, with insects, and really empathize with them, and then go on to reptiles and so forth. Other human beings and yourself will all follow.
On the other hand, if you murder little insects and dismiss any possibility of their wanting pleasure and avoiding pain, then when you come to animals that are more and more like us, it's easy to dismiss them. Even if a dog is wounded and it yelps, you don't experience the pain. Since you've already gotten into the mode of disregarding the pleasure and pain of an insect, now it's easier to disregard a bird, a dog, and even another person who cries out. With the attitude "I don't feel it," you dismiss that pain. You would never feel the empathy until it actually hits your own skin.
If you have greater sensitivity to the pain and suffering of animals, then all the more you will have a greater sensitivity and empathy toward other human beings. It is a uniquely Buddhist phrase to refer to other sentient beings as "mother sentient beings." The point is, how you perceive sentient beings makes a difference.— His Holiness The Dalai Lama in The Dalai Lama by Daniel Goleman